The Ukrainian, who missed Chelsea's FA Cup victory over Manchester United on Saturday night because of a groin injury, has failed to reproduce the kind of form which justified his record $74 million signing from AC Milan in May 2006.
But as Beckham prepares to head for Los Angeles Galaxy, the 30-year-old Shevchenko revealed that he too would like to try his hand on the other side of the Atlantic.
"I'd like to play there, actually," Shevchenko told Sports Illustrated.com.
"Soccer is growing in the US and I would like to be a part of that.
"I played there last summer against the Major League Soccer All-Stars and I saw that it is definitely improving."
Shevchenko believes that playing out of position for Chelsea did not help him during a difficult opening season at Stamford Bridge.
"I didn't play in my position this year," he added. "I wasn't the key of the attack.
"I was playing further behind, away from goal, which is different from how I played at Milan and maybe that's why Didier Drogba scored so many goals this year.
"We made a good partnership with me setting him up some of the time. At Milan I played in my natural role. Here I had to adapt to be something else and I did it so I could help the team.
"It wasn't a great season but it hasn't been the worst," he said.
"The main priority for me is feeling well next season."
"People always expect a lot from me. I wasn't well in the first four months, partly because of fatigue from the World Cup and partly because of the injury I was carrying.
"But then I had a good stretch in the middle of the season. In the end, despite everything, I ended up with 14 goals and 11 or 12 assists - and that's not a bad season.
"I know people wanted 30 goals a season but the reality is that it can't happen every season. With all the problems I had, I don't think I did that badly.
"Now the season is over for Chelsea I would like to think things are going to get sorted out and I am hopeful we will be in talks. SOURCE: © 2007 Australian Broadcasting Corporation